Abstract
The expanded lever rule is more efficient for calculating phase volume fraction when two phases are partly overlapped. It can make up the deficiency of metallography analysis when phases are similar in morphology. In this study, the expanded lever rule on the phase transformation rate curve is introduced, the approximate symmetry principle in applying the expanded lever rule is modified, and the resulting measurement uncertainty is discussed. Results show that (i) the calculated volume fraction of pearlite by the expanded lever rule in an overlapped two-phase process of a high strength low alloy (HSLA) weld metal is in accordance with the result by metallography analysis, and (ii) the expanded lever rule has an advantage over metallography analysis as it can calculate upper bainite, lower bainite, and lath-like martensite volume fractions in a three-phase process with two overlaps of a HSLA steel. The expanded lever rule is applicable to overlapped two-phase processes of any material theoretically since each phase process can be described by Johnson–Mehl–Avrami–Kolmogorov equation.
Similar content being viewed by others
References
[1] Y. Liu, D. Wang, F. Sommer, E.J. Mittemeijer: Acta Mater., 2008, vol. 56, pp. 3833-42.
[2] C.M. Garzón, A.J. Ramirez: Acta Mater., 2006, vol. 54, pp. 3321-31.
[3] X. Yu, J.L. Caron, S.S. Babu, J.C. Lippold, D. Isheim, D.N. Seidman: Acta Mater., 2010, vol. 58, pp. 5596-09.
[4] J.E. Hilliard, J.W. Cahn: Trans. Metall. Soc. AIME, 1961, vol. 221, pp. 344-52.
[5] R.L. Higginson, C.M. Sellars: Worked examples in quantitative metallography, Maney Pub., London, LON, 2003, pp. 13-14.
M. Gomez, S.F. Medina, G. Caruana: ISIJ Int., 2003, vol. 43, pp. 1228-37.
[7] R. Petrov, L. Kestens, Y. Houbaert: Mater. Charact., 2004, vol. 53, pp.51-61.
[8] X.W. Lei, J.H. Huang, S.H. Chen, X.K. Zhao: Metall. Mater. Trans. A, 2016, vol. 47A, pp. 2795–03.
[9] M.S.A. Karunaratne, S. Kyaw, A. Jones, R. Morrell, R.C. Thomson: J. Mater. Sci., 2016, vol. 51, pp. 4213-26.
[10] J.A. Monroe, D. Gehring, I. Karaman, R. Arroyave, D.W. Brown, B. Clausen: Acta Mater., 2016, vol. 102, pp.333-41.
[11] E. Woldt: J. Phys. Chem. Solids, 1992, vol. 53, pp. 521-27.
[12] J.S. Blázquez, C.F. Conde, A. Conde: Acta Mater., 2005, vol. 53(8), pp. 2305-11.
[13] X.W. Lei, J.H. Huang, S.H. Chen, X.K. Zhao: Mater. Lett., 2016, vol.181, pp. 240-43.
[14] International Organization for Standardization: Guide to the Expression of Uncertainty in Measurement, 1st ed., International Organization for Standardization, Geneva, 1995, pp. 16.
[15] X.W. Lei, J.H. Huang, S.H. Chen, X.K. Zhao: Metall. Mater. Trans. A, 2016, vol. 48(1), pp. 198-07.
Acknowledgments
This work was supported by the Science and Technology Project of the Education Department of Jiangxi Province of China [Grant Number GJJ180481] and National Natural Science Foundation of China [Grant Numbers 51904125, 51804138, 51871114, 51664021, and 51974139].
Author information
Authors and Affiliations
Corresponding authors
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Manuscript submitted January 21, 2020.
Rights and permissions
About this article
Cite this article
Lei, XW., Yang, RB., Xiao, LL. et al. The Expanded Lever Rule on the Phase Transformation Rate Curve for Phase Volume Fraction Calculation in Thermal Simulations. Metall Mater Trans A 51, 5049–5055 (2020). https://doi.org/10.1007/s11661-020-05902-1
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11661-020-05902-1